Question

A telescope has an objective lens of $10 \,cm$ diameter and is situated at a distance of one kilometre from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is $5000 \,?$, of the order of

• A. 0.5 m
• B. 5 m
• C. 5 mm
• D. 5 cm

Answer 1

Answer: (C)

5 mm

Answer 2

Resolving limit of telescope is $\theta \propto \frac{x}{D}=\frac{\lambda}{d}$ $\Rightarrow x=\frac{\lambda D}{d}$ Given, $\lambda=5000\, ?=5000 \times 10^{-10} m$ $D=1 \,km =1000\, m$ $d=10\, cm =0.1\, m$ Hence, $x =\frac{5000 \times 10^{-10} \times 1000}{0.1}$ $=5 \times 10^{-3} m$ $=5 \,mm$